Theorem bj-alalbial 35579

Description: Adding a second quantifier over the same variable is a transparent operation, (∀∀ case). (Contributed by BJ, 20-Oct-2019.)

Assertion

Ref	Expression
bj-alalbial	⊢ (∀𝑥∀𝑥𝜑 ↔ ∀𝑥𝜑)

Proof of Theorem bj-alalbial

Step	Hyp	Ref	Expression
1		nfa1 2149	. 2 ⊢ Ⅎ𝑥∀𝑥𝜑
2	1	19.3 2196	1 ⊢ (∀𝑥∀𝑥𝜑 ↔ ∀𝑥𝜑)

Syntax hints:   ↔ wb 205  ∀wal 1540

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1914  ax-6 1972  ax-7 2012  ax-10 2138  ax-12 2172

This theorem depends on definitions:  df-bi 206  df-or 847  df-ex 1783  df-nf 1787

This theorem is referenced by: (None)